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12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

Chapter 14, Problem 2RE

Textbook Problem

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What is the domain of

To determine

**To calculate:** The domain of the function

**Given Information:**

The provided function is

**Formula used:**

The domain of a function of two variables

If the function maps each element of the domain to an element in the codomain, then it is said to be well defined.

To find the domain of a rational function, set the denominator of the function equals to zero. Then the domain of the function is the set of all ordered pairs except the values for which the denominator is zero.

The function

**Calculation:**

Consider the provided function,

Rewrite

Thus,

The function

Recall that, to find the domain of a rational function, set the denominator of the function equals to zero. Then the domain of the function is the set of all ordered pairs except the values for which the denominator is zero

Mathematical Applications for the Management, Life, and Social Sciences

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Ch. 14.1 - CHECKPOINT
1. Find the domain of the function
Ch. 14.1 - CHECKPOINT
2. (a) If .
(b) If .
Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...

Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - 23. Investment The future value S of an investment...Ch. 14.1 - 24. Amortization If $100,000 is borrowed to...Ch. 14.1 - 25. Curve speeds One method traffic planners use...Ch. 14.1 - 26. Wilsons lot size formula In economics, the...Ch. 14.1 - Temperature-humidity models The “feels like”...Ch. 14.1 - Temperature-humidity models The “feels like”...Ch. 14.1 - 29. Mortgage The following tables show that a...Ch. 14.1 - 30. Wind chill Wind and cold temperatures combine...Ch. 14.1 - 31. Utility Suppose that the utility function for...Ch. 14.1 - 32. Utility Suppose that an indifference curve for...Ch. 14.1 - 33. Production Suppose that a company’s production...Ch. 14.1 - 34. Production Suppose that a company’s production...Ch. 14.1 - 35. Production Suppose that the number of units of...Ch. 14.1 - 36. Profit The Kirk Kelly Kandy Company makes two...Ch. 14.1 - 37. Epidemic The cost per day to society of an...Ch. 14.1 - 38. Pesticide An area of land is to be sprayed...Ch. 14.2 - CHECKPOINT
1. If , find the following.
(a)
(b)
Ch. 14.2 - CHECKPOINT
2. If , find the following.
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3.
(a) (b) (c) (d)
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4. ,find the following.
(a) zxx (b) zyy...Ch. 14.2 - CHECKPOINT
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16. If
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17. Find the partial derivative of
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with...Ch. 14.2 -
19. Find the slope of the tangent in the...Ch. 14.2 -
20. Find the slope of the tangent in the...Ch. 14.2 -
21. Find the slope of the tangent in the...Ch. 14.2 -
22. Find the slope of the tangent in the...Ch. 14.2 -
23. If , find the following.
(a) (b) (c)...Ch. 14.2 -
24. If , find the following.
(a) (b) (c)
Ch. 14.2 -
25. If , find the following.
(a) (b) (c)
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26. If , find the following.
(a) (b) (c)
Ch. 14.2 -
27. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
28. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
29. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
30. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
31. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 - 32. If , find the following.
(a) (b) (c) (d)
Ch. 14.2 - 33. If , find the following.
Ch. 14.2 - 34. If , find the following.
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Ch. 14.2 - .
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Ch. 14.2 -
Ch. 14.2 - 45. Mortgage When a homeowner has a 25-year...Ch. 14.2 - 46. Mass transportation ridership Suppose that in...Ch. 14.2 - 47. Wilson's lot size formula In economics, the...Ch. 14.2 - 48. Cost Suppose that the total cost (in dollars)...Ch. 14.2 - 49. Pesticide Suppose that the number of thousands...Ch. 14.2 - 50. Profit Suppose that the profit (in dollars)...Ch. 14.2 - 51. Utility If is the utility function for goods...Ch. 14.2 - 52. Utility If the utility function for goods X...Ch. 14.2 - 53. Production Suppose that the output Q (in...Ch. 14.2 - 54. Production Suppose that the production Q (in...Ch. 14.2 - Wind chill Dr. Paul Siple conducted studies...Ch. 14.2 - Wind chill Dr. Paul Siple conducted studies...Ch. 14.3 - CHECKPOINT
If the joint cost in dollars for two...Ch. 14.3 - CHECKPOINT
2. If the production function for a...Ch. 14.3 - CHECKPOINT
3. If the demand functions for two...Ch. 14.3 - 1. The cost (in dollars) of manufacturing one item...Ch. 14.3 - 2. The manufacture of 1 unit of a product has a...Ch. 14.3 - 3. The total cost of producing 1 unit of a product...Ch. 14.3 - 4. The total cost of producing an item is
...Ch. 14.3 - 5. The total cost of producing 1 unit of a product...Ch. 14.3 - 6. The total cost of producing 1 unit of a product...Ch. 14.3 - 7. The joint cost (in dollars) for two products is...Ch. 14.3 - 8. The joint cost (in dollars) for products X and...Ch. 14.3 - 9. If the joint cost function for two products is
...Ch. 14.3 - 10. Suppose the joint cost function for x units of...Ch. 14.3 - 11. Suppose that the joint cost function for two...Ch. 14.3 - 12. Suppose that the joint cost function for two...Ch. 14.3 - 13. Suppose that the production function for a...Ch. 14.3 - 14. Suppose the production function for a product...Ch. 14.3 - 15. Suppose that the production function for a...Ch. 14.3 - 16. Suppose that a company’s production function...Ch. 14.3 - For Problems 17-19, suppose that the number of...Ch. 14.3 - For Problems 17-19, suppose that the number of...Ch. 14.3 - For Problems 17-19, suppose that the number of...Ch. 14.3 - 20. If a production function is given by , find...Ch. 14.3 - 21. Suppose the Cobb-Douglas production function...Ch. 14.3 - 22. Suppose the Cobb-Douglas production function...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.4 - CHECKPOINT
Suppose that
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Suppose that
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Suppose that .
3. Test the point(s) for...Ch. 14.4 - CHECKPOINT
4. Use linear regression to write the...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 17 and 18, use the points given in the...Ch. 14.4 - In Problems 17 and 18, use the points given in the...Ch. 14.4 - 19. Profit Suppose that the quarterly profit from...Ch. 14.4 - 20. Profit The profit from the sales of two...Ch. 14.4 - 21. Nutrition A new food is designed to add weight...Ch. 14.4 - 22. Profit The profit for a grain crop is related...Ch. 14.4 - 23. Production Suppose that
tons
is the...Ch. 14.4 - 24. Production Suppose that x units of one input...Ch. 14.4 - 25. Profit Suppose that a manufacturer produces...Ch. 14.4 - 26. Profit Suppose that a firm produces two...Ch. 14.4 - 27. Manufacturing Find the values for each of the...Ch. 14.4 - 28. Manufacturing Find the values for each of the...Ch. 14.4 - 29. Profit A company manufactures two products, A...Ch. 14.4 - 30. Production Let x be the number of work-hours...Ch. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - 33. Modeling U.S. National consumption The...Ch. 14.4 - 34. Modeling Retirement benefits The following...Ch. 14.4 - 35. Modeling World population The table gives the...Ch. 14.4 - 36. Modeling Student loans The following table...Ch. 14.5 - CHECKPOINT
Find the minimum value of
1. forming...Ch. 14.5 - CHECKPOINT
Find the minimum value of , subject to...Ch. 14.5 - CHECKPOINT
Find the minimum value of
3. setting...Ch. 14.5 - CHECKPOINT
Find the minimum value of
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Ch. 14.5 - 3. Find the minimum value of subject to the...Ch. 14.5 - 4. Find the maximum value of subject to the...Ch. 14.5 - 5. Find the maximum value of subject to .
Ch. 14.5 - 6. Find the maximum value of the function subject...Ch. 14.5 - 7. Find the maximum value of the function subject...Ch. 14.5 - 8. Find the minimum value of subject to the...Ch. 14.5 - 9. Find the maximum value of subject to .
Ch. 14.5 - 10. Find the maximum value of subject to .
Ch. 14.5 - 11. Find the minimum value of subject to the...Ch. 14.5 - 12. Find the minimum value of subject to the...Ch. 14.5 - 13. Find the maximum value of subject to the...Ch. 14.5 - 14. Find the maximum value of subject to the...Ch. 14.5 - 5. Utility Suppose that the utility function for...Ch. 14.5 - 16. Utility Suppose that the budget constraint in...Ch. 14.5 - 17. Utility Suppose that the utility function for...Ch. 14.5 - 18. Utility Suppose that the utility function for...Ch. 14.5 - 19. Production Suppose a company has the...Ch. 14.5 - 20. Production Suppose a company has the...Ch. 14.5 - 21. Cost A firm has two plants, X and Y. Suppose...Ch. 14.5 - 22. Cost Suppose that the cost of producing x...Ch. 14.5 - 23. Revenue On the basis of past experience, a...Ch. 14.5 - 24. Manufacturing Find the dimensions x, y, and z...Ch. 14.5 - 25. Manufacturing Find the dimensions (in...Ch. 14.5 - 26. Manufacturing Show that a box with a square...Ch. 14 - 1. What is the domain of ?
Ch. 14 - 2. What is the domain of ?
Ch. 14 - 3. If .
Ch. 14 - 4. If .
Ch. 14 - 5. Find .
Ch. 14 - 6. Find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - 13. Find the partial derivative of with respect...Ch. 14 - 14. Find the slope of the tangent in the...Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 19 and 20, find each function’s...Ch. 14 - In Problems 19 and 20, find each function’s...Ch. 14 - 21. Find the maximum value of subject to the...Ch. 14 - 22. Find the maximum value of subject to the...Ch. 14 - 23. Utility Suppose that the utility function for...Ch. 14 - 24. Savings plans The accumulated value A of a...Ch. 14 - 25. Retirement benefits The monthly benefit B (in...Ch. 14 - 26. Advertising and sales The number of units of...Ch. 14 - 27. Cost The joint cost, in dollars, for two...Ch. 14 - 28. Production Suppose that the production...Ch. 14 - 29. Marginal demand The demand functions for...Ch. 14 - 30. Marginal demand Suppose that the demand...Ch. 14 - 31. Profit The weekly profit (in dollars) from the...Ch. 14 - 32. Cost Suppose a company has two separate plants...Ch. 14 - 33. Utility If the utility function for two...Ch. 14 - 34. Production Suppose a company has the...Ch. 14 - 35. Modeling US. average wage The table gives the...Ch. 14 - 36. Modeling Civilian workforce The following...Ch. 14 - 1. Consider the function .
(a) Find the domain of...Ch. 14 - 2. Find all first and second partial derivatives...Ch. 14 - 3. Let . Find the pairs that are critical points...Ch. 14 - 4. Suppose a company’s monthly production value Q...Ch. 14 - 5. The monthly payment R on a loan is a function...Ch. 14 - 6. Let . Find .
Ch. 14 - 7. Suppose the demand functions for two products...Ch. 14 - 8. Suppose a store sells two brands of disposable...Ch. 14 - 9. Find x and y that maximize the utility function...Ch. 14 - 10. Modeling In the last half of the twentieth...

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